Question

Galactic Astrophysics:

We observe a fractional shift in the spectral lines from a distant elliptical galaxy such that the ratio of observed and emitted wavelengths:
$( \lambda _o / \lambda _e ) = 3$
How much smaller was the Universe when the light was emitted by the elliptical galaxy?

Answer 1

Page-1 we know redshift is a phenomenon where Electromagnetic radiation from an object undergoes an increase in wavelength and we know cosmological red shift [For FLRW space time] 1 + z = a_now/a_then and to drive red shift effect, using geodisec equation for FLRW Space time dS^2 = 0 = -C^2 dt^2 + a^2 dr^2/1 - K r^2 dS = spae time dt = time interval C = Speed of light a = time-displacement cosmic scale factor K = Curvature per unit area an observer observing the crest of light wave at a position r = 0 and time t = t_now, the crest of the light wave was emitted at a time t = t_then in the past and a distant position r = R C integral^t_now_t_then dt/a = integral^0_R dr/squareroot 1 - K r^2 -(2) therefore t = t_then + lambda_then/C rightdoublearrow time for next emitted crest and t = t_now + lambda_now/C rightdoublearrow time to observe that next crest